Not an old warhorse, but offering something new each time, as one critic said of 23 year-old American composer Samuel Barber's masterpiece. Barber himself got a bit tired of its success, the price of peaking early.
Leonard Bernstein takes it slowly as he conducts the New York Philharmonic. Contemplation for a summer's evening.
In their recent ICM address, Dan Halpern-Leistner and Jarod Alper posed the question: does the stack of canonically polarized curves admit a theta-stratification whose semistable locus is the moduli space of stable curves? In other, perhaps more familiar, language: is there some notion for curves that understands instability the way Harder-Narasimhan type does for vector bundles/coherent sheaves?
I will explain some joint work with Dave Swinarski that solves the analogous problem for certain rational curves, and then sketch out an argument that I think should solve the problem in general.
